The growth of the range of stable random walks

Wojciech Cygan; Nikola Sandrić; Stjepan Sebek

The growth of the range of stable random walks

Wojciech Cygan, Nikola Sandrić, Stjepan Sebek

Institute of Discrete Mathematics (5050)

Research output: Contribution to journal › Article

Abstract

In this article, we establish an almost sure invariance principle for the capacity
and cardinality of the range for a class of α-stable random walks on the integer
lattice Z^d with d > 5α/2 and d > 3α/2, respectively. As a direct consequence, we
conclude Khintchine's and Chung's laws of the iterated logarithm for both processes.

Original language	English
Number of pages	16
Journal	arXiv.org e-Print archive
Publication status	Submitted - 2019

Keywords

The range of a random walk
Capacity
An almost sure invariance principle
The law of the iterated logarithm

ASJC Scopus subject areas

Mathematics(all)

Access to Document

https://arxiv.org/abs/1910.09831

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abstract = "In this article, we establish an almost sure invariance principle for the capacityand cardinality of the range for a class of α-stable random walks on the integerlattice Zd with d > 5α/2 and d > 3α/2, respectively. As a direct consequence, weconclude Khintchine's and Chung's laws of the iterated logarithm for both processes.",

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AU - Cygan, Wojciech

AU - Sandrić, Nikola

AU - Sebek, Stjepan

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N2 - In this article, we establish an almost sure invariance principle for the capacityand cardinality of the range for a class of α-stable random walks on the integerlattice Zd with d > 5α/2 and d > 3α/2, respectively. As a direct consequence, weconclude Khintchine's and Chung's laws of the iterated logarithm for both processes.

AB - In this article, we establish an almost sure invariance principle for the capacityand cardinality of the range for a class of α-stable random walks on the integerlattice Zd with d > 5α/2 and d > 3α/2, respectively. As a direct consequence, weconclude Khintchine's and Chung's laws of the iterated logarithm for both processes.

KW - The range of a random walk

KW - Capacity

KW - An almost sure invariance principle

KW - The law of the iterated logarithm

M3 - Article

JO - arXiv.org e-Print archive

JF - arXiv.org e-Print archive

ER -